A Maxwell material is a viscoelastic material having the properties both of elasticity and viscosity. It is named for James Clerk Maxwell who proposed the model in 1867. It is also known as a Maxwell fluid.
The Maxwell model can be represented by a purely viscous damper and a purely elastic spring connected in series, as shown in the diagram. In this configuration, under an applied axial stress, the total stress, σTotal and the total strain, can be defined as follows:
- σTotal = σD = σS
where the subscript D indicates the stress/strain in the damper and the subscript S indicates the stress/strain in the spring. Taking the derivative of strain with respect to time, we obtain:
If we connect these two elements in parallel, we get a model of Kelvin-Voigt material.
In a Maxwell material, stress σ, strain ε and their rates of change with respect to time t are governed by equations of the form:
or, in dot notation:
The equation can be applied either to the shear stress or to the uniform tension in a material. In the former case, the viscosity corresponds to that for a Newtonian fluid. In the latter case, it has a slightly different meaning relating stress and rate of strain.
The model is usually applied to the case of small deformations. For the large deformations we should include some geometrical non-linearity. For the simplest way of generalizing the Maxwell model, refer to the Upper Convected Maxwell Model.
Effect of a sudden deformation
If a Maxwell material is suddenly deformed and held to a strain of , then the stress decays with a characteristic time of .
The picture shows dependence of dimensionless stress upon dimensionless time :
If we free the material at time t1, then the elastic element will spring back by the value of
Since the viscous element would not return to its original length, the irreversible component of deformation can be simplified to the expression below:
Effect of a sudden stress
If a Maxwell material is suddenly subjected to a stress σ0, then the elastic element would suddenly deform and the viscous element would deform with a constant rate:
If at some time t1 we would release the material, then the deformation of the elastic element would be the spring-back deformation and the deformation of the viscous element would not change:
The Maxwell Model does not exhibit creep since it models strain as linear function of time.
If a small stress is applied for a sufficiently long time, then the irreversible stresses become large. Thus, Maxwell material is a type of liquid.
The complex dynamic modulus of a Maxwell material would be:
Thus, the components of the dynamic modulus are :
The picture shows relaxational spectrum for Maxwell material. The relaxation time constant is .
Blue curve dimensionless elastic modulus Pink curve dimensionless modulus of losses Yellow curve dimensionless apparent viscosity X-axis dimensionless frequency ωλ.
Wikimedia Foundation. 2010.
Look at other dictionaries:
Maxwell Render — Sample Maxwell Render image output by Benjamin Brosdaux … Wikipedia
Maxwell Montes — Radar image of Maxwell Montes Feature type Mountain range Coordinates … Wikipedia
Maxwell Air Force Base — Part of Air Education and Training Command (AETC) Located near: Montgomery, Alabama … Wikipedia
Maxwell (crater) — Coordinates 30°12′N 98°54′E / 30.2°N 98.9°E / … Wikipedia
Maxwell Caulfield — Born 23 November 1959 (1959 11 23) (age 51) Duffield, Derbyshire, England Other names Maxwell Findlater Occupation Actor … Wikipedia
Maxwell Render — Тип система рендеринга Разработчик Next Limit Technologies Операционная система Microsoft Windows, Mac OS X, Linux Последняя версия 2.7.2 (27 ноября 2012) … Википедия
Maxwell R. Thurman — General Maxwell Reid Thurman Nickname Mad Max … Wikipedia
Maxwell Montes — es una montaña de la superficie de Venus. Se encuentra en las coordenadas 65° de latitud norte y 6° de longitud este del planeta, en la altiplanicie de Ishtar Terra. Fotografía por radar de Maxwell Montes Es el punto más alto de Venus, alcanzado… … Wikipedia Español
Maxwell National Wildlife Refuge — IUCN Category IV (Habitat/Species Management Area) … Wikipedia
Maxwell the Magic Cat — was a comic strip written and drawn by Alan Moore under the pseudonym Curt Vile (a pun on the name of composer Kurt Weill), with a friend Steve Moore under the pseudonym Jill de Ray (in parody of Gilles de Rais, a French murderer). Publication It … Wikipedia